Question

If A ⊂ B, then which of the following describes the relationship between A and B?

Answer 1

The answer is 4 alone, or 1 and 4, depending on how you interpret the symbol (see below for explanation).

The writing $A \subset B$ means that A is a subset of B. This means that every element of A is also an element of B, while there are elements of B that are not elments of A. For example, even numbers are a subset of natural numbers: all even numbers are natural numbers, but not all natural numbers are even.

In theory, a subset could "fill" the whole superset (and thus they are the same set), but this is indicated by the writing $A \subseteq B$. Nevetheless, sometimes the two symbols are interchanged, and one writes $A \subset B$ but means $A \subseteq B$.

You can think of this as the same difference between  $x$ and $x \leq y$

So, the first point is false if you mean that A is a "strict" subset of B, while it can be true if you mean that A is generally a subset of B.

As for the second point, set B can't have less elements than set A. In this case, there would be an element in A not belonging to B, which is impossibile because B is a superset of A.

Third point: the intersection can't be the empty set (unless A is empty), because every element in A also belongs to be, and so the intersection between A and B is actually A itself.

Finally, the fourth point is true: basing on everything we said so far, B contains at least all the elements in A, and possibly some more.